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Mathematics - cube root

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martinjr | 12:09 Thu 10th Nov 2011 | Quizzes & Puzzles
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Can any member provide a method for calculating a cube root for numbers with 4 or more digits, e.g., 2345, 23456, 234567 etc?
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http://www.wikihow.co...ate-Cube-Root-by-Hand

Having said that, found this which seems to work!
22:20 Sat 12th Nov 2011
Are you allowed to use a calculator or spreadsheet?
Do you know a method for a number that has fewer than 3 digits because I don't.
I can do square roots in my head and on paper using iteration but not cube roots
I can do cube roots by iteration too but I need a basic calculator (no cube root key) to do some division. Is that acceptable? To how many decimal places do you need to be able to work the answer out?
Log Tables?
Just a thought ........... am I right in saying that if the 4 digit number ends in 7, then the cube root must end in 3
If it ends in 5 then the cube root must end in 5 etc etc
Then divide by the factor, and go from there ........... not sure where though :o(
2345
Take an estimate: say 12
Calculate 2345/(12 x12)
That is 16.285.
Add your estimate twice to 16.285. That is 40.285.
Divide that by 3: that gives 13.428

Repeat using 13.428 as your guess

2345/(13.428x13.428) = 13.005
Add that to 13.428 +13.428.
That gives 39.861
Divide it by 3. Gives 13.287
That is pretty much the cube root (I think the answer is 13.286)
the last digit of the cube can only give you the last digit of the root, that digit is not a factor

e.g. 13³ = 2197 but neither 3 nor 7 are factors
Number ends in 0 then cube root must end in 0
1 1
2 8
3 7
4 4
5 5
6 6
7 3
8 2
9 9
........... oh poop Bibbles .............. you're right not necessarily a factor :o(
The tricks suggested, ie looking at the last digit, won't help as the OPer isn't asking just about cubes of integers. He gave example 2345 whiuch has a cube root 13.285593158578324, wich I found using http://www.csgnetwork...cuberootcubecalc.html
Just Google "Cube root of xxxx" and the answer will appear at the top of the page. Save the grey cells.
I assumed martinjr wanted a method for any number with more than 4 digits and had just used numbers with consecutive digits for his examples.

Hi the builder- what you say works the other way round but not always your way round. So yes if you take a number ending in 5 its cube will also end in 5
Similarly the cube of a number ending in 8 will end with a 2.

But it doesn't always work in reverse. The cube root of 2345 doesn't end in a 5 because the answer is not a whole number
I think my method should always work but you need a calculator. Certainly if I'd done a third iteration I'd have got the answer to at least 3 decimal places
There is a way using a long division technique similar to one that can be used to find square roots, but I found out about it so long ago that I can't recall the details (yet).
23456
Estimate is 25
23456/(25x25)=37.53
(37.53+25+25)/3= 29.177

Repeat using 29.177 as estimate
23456/(29.177x29.177)= 27.553
(27.553+29.177+29.177)/3 = 28.63

Correct to 2 decimal places. Check it on Excel
I was hoping matinjr might have returned to this thread,
Question Author
I've just returned to my thread right now (Sat 12th @17.46). Lots of interesting replies but factor30 is correct in assuming what I needed was a method for calculating the cube root of any number with more than 4 digits. I'm really only looking for the old arithmetic method which involved splitting the number into sets of three but the method escapes me. If it helps:- calculating the square root involves splitting the number into pairs and bringing down next pair alongside the remainder after finding the square of 1st pair of numbers. I know I've explained this badly so sorry about that.
I'm not sure there is a chunking method, similar to square roots, I will now be up all night trying! Thanks!
http://www.wikihow.co...ate-Cube-Root-by-Hand

Having said that, found this which seems to work!
Question Author
Thanks for that Zebo. You need not stay up all night after all but I will trying to prove that Wikihow is correct!!

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